The present invention is related to detecting process variations in integrated circuits, and more specifically to the detection of and compensation for process variations in resistors in integrated circuits.
Integrated circuits often include dozens, hundreds, or millions of electronic components. Resistors in integrated circuits are usually implemented using either diffused regions in the silicon substrate or depositing thin films on the wafer surface. Resistors in integrated circuits can be formed in a variety of patterns, such as straight patterns or right angled zig-zag patterns, from individual square or rectangular resistive areas. Regardless of the pattern, the resistance of the resistor depends on the dimensions and number of the resistive areas included in the resistor. For purposes of explanation, the resistor may be considered a rectangle.
It is known in the integrated circuit fabrication field that the resistance of a resistor in an integrated circuit is related to the dimensions of the resistor and the resistivity of the material used to create the resistor. The resistance of a resistor in an integrated circuit equals the sheet resistance of the material used to form the resistor multiplied by the length of the resistor and divided by the width of the resistor. The sheet resistance is simply the resistivity of the material used divided by the depth of the resistor. Therefore, the resistance of a particular resistor varies inversely with its width, i.e., as width increases, resistance decreases and as width decreases, resistance increases.
Analog circuit designs often depend upon well defined resistor values for proper operation. In practice, the actual resistance of a resistor may vary from a design target width due to process variations that occur during fabrication. Component values can vary greatly, even within the acceptable tolerances for process variations. Because of process variations, it is difficult to control the width of a resistor designed to have a narrow width within tolerances which prevent appreciable modification in resistance. Increasing the width of such a resistor limits this effect, but if the target resistance value is high, the overall size of the resistor becomes unacceptably large due to the increased length needed to achieve the high resistance value.
The most common technique for making a design immune to resistance variation is to use matching resistors which track each other for process variations. This technique is generally useful, but it requires having identical resistors. Process variations tend to occur rather uniformly throughout a substrate, but differences may occur between specific locations on a substrate. Resistors which are matched to each other undergo equivalent changes in resistance from a design resistance due to process variations. Balancing resistors are usually placed in different part of a circuit with the thought that the effect of variations will track in each. The balance essentially cancels out the effect of the variation as the circuit is designed to be sensitive only to the overall balance, not the actual resistance. This technique, however, is less effective when matching narrow resistors because any non-uniform process variations have a greater effect on narrow resistors and impair the ability of a first narrow resistor to track a second narrow resistor, particularly if the narrow resistors are disposed remote from each other on the substrate.
A drawback to the matching technique is that it requires resistors matched to each other to have the same widths, and a narrow resistor, therefore, cannot be effectively matched to a wide resistor because the resistance of the narrow resistor is affected by process variations, such as process width variations, more than the resistance of the wide resistor. This inability to track each other leads to matching errors, which may limit circuit performance. As mentioned, making all of the resistors wide enough to avoid this problem may result in unacceptably large resistors and area sacrifices on the substrate on which the integrated circuit is formed. Also as mentioned, resistors may be matched to each other, but any non-uniform width variations in resistors across a substrate effect narrow resistors that are matched to each other more so than wide resistors that are matched to each other.
It is desirable to match a wide resistor to a narrow resistor rather than pay the area overhead of both resistors having large widths. Therefore, there is a need to be able to determine the amount of process width variation for resistors in an integrated circuit and to account for this variation without relying on matching resistors having identical design widths.
The present invention comprises a method and apparatus for determining whether an actual width of a resistor in an integrated circuit varies from a design width. A reference resistor having a reference resistor design width and a test resistor having a test resistor design width are provided in an integrated circuit. The reference resistor and the test resistor are sized to have substantially equal resistances at their respective design widths. The reference resistor design width is sized such that the reference resistor is less susceptible than the test resistor to resistance changes due to variations from design width in resistors in the integrated circuit. Substantially equal currents flow from current sources through the test resistor and the reference resistor. A comparator detects a reference voltage across the reference resistor and a test voltage across the test resistor. The output of comparator indicates that the actual width of the test resistor varies from the actual width of the test resistor design width if the reference voltage and the test voltage are not substantially equal.
The method and apparatus may be used to determine an amount of process width variation occurring between the design width of a resistor and the resistor""s actual width. This determination may be used to account for process width variations in an integrated circuit and allow matching of resistors in an integrated circuits having different design widths. This, in turn, provides area conservation in integrated circuits. In one embodiment of the present invention, the determined process width variation is used to match resistors in an integrated digital to analog converter.
The above and other features of the present invention will be better understood from the following detailed description of the preferred embodiments of the invention which is provided in connection with the accompanying drawings.